DOCSLIB.ORG

Introductory Quantum Optics

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Introductory Quantum Optics This page intentionally left blank Introductory Quantum Optics This book provides an elementary introduction to the subject of quantum optics, the study of the quantum-mechanical nature of light and its interaction with matter. The presentation is almost entirely concerned with the quantized electromag- netic field. Topics covered include single-mode field quantization in a cavity, quantization of multimode fields, quantum phase, coherent states, quasi- probability distribution in phase space, atom–field interactions, the Jaynes– Cummings model, quantum coherence theory, beam splitters and interferom- eters, nonclassical field states with squeezing etc., tests of local realism with entangled photons from down-conversion, experimental realizations of cavity quantum electrodynamics, trapped ions, decoherence, and some applications to quantum information processing, particularly quantum cryptography. The book contains many homework problems and a comprehensive bibliography. This text is designed for upper-level undergraduates taking courses in quantum optics who have already taken a course in quantum mechanics, and for first- and second-year graduate students. A solutions manual is available to instructors via [email protected]. C G is Professor of Physics at Lehman College, City Uni- versity of New York.He was one of the first to exploit the use of group theoretical methods in quantum optics and is also a frequent contributor to Physical Review A.In1992 he co-authored, with A. Inomata and H. Kuratsuji, Path Integrals and Coherent States for Su (2) and SU (1, 1). P K is a leading figure in quantum optics, and in addition to being President of the Optical Society of America in 2004, he is a Fellow of the Royal Society. In 1983 he co-authored Concepts of Quantum Optics with L. Allen. He is currently Head of the Physics Department of Imperial College and Chief Scientific Advisor at the UK National Physical Laboratory. Introductory Quantum Optics Christopher Gerry Lehman College, City University of New York Peter Knight Imperial College London and UK National Physical Laboratory cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge cb2 2ru, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521820356 © C. C. Gerry and P. L. Knight 2005 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2004 isbn-13 978-0-511-22949-7 eBook (EBL) isbn-10 0-511-22949-6 eBook (EBL) isbn-13 978-0-521-82035-6 hardback isbn-10 0-521-82035-9 hardback isbn-13 978-0-521-52735-4 paperback isbn-10 0-521-52735-x paperback Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. C. C. G. dedicates this book to his son, Eric. P. L. K. dedicates this book to his wife Chris. Contents Acknowledgements page xii 1 Introduction1 1.1 Scope and aims of this book1 1.2 History2 1.3 The contents of this book7 References8 Suggestions for further reading8 2 Field quantization 10 2.1 Quantization of a single-mode field 10 2.2 Quantum fluctuations of a single-mode field 15 2.3 Quadrature operators for a single-mode field 17 2.4 Multimode fields 18 2.5 Thermal fields 25 2.6 Vacuum fluctuations and the zero-point energy 29 2.7 The quantum phase 33 Problems 40 References 41 Bibliography 42 3 Coherent states 43 3.1 Eigenstates of the annihilation operator and minimum uncertainty states 43 3.2 Displaced vacuum states 48 3.3 Wave packets and time evolution 50 3.4 Generation of coherent states 52 3.5 More on the properties of coherent states 53 3.6 Phase-space pictures of coherent states 56 3.7 Density operators and phase-space probability distributions 59 3.8 Characteristic functions 65 Problems 71 References 72 Bibliography 73 vii viii Contents 4 Emission and absorption of radiation by atoms 74 4.1 Atom–field interactions 74 4.2 Interaction of an atom with a classical field 76 4.3 Interaction of an atom with a quantized field 82 4.4 The Rabi model 87 4.5 Fully quantum-mechanical model; the Jaynes–Cummings model 90 4.6 The dressed states 99 4.7 Density-operator approach: application to thermal states 102 4.8 The Jaynes–Cummings model with large detuning: a dispersive interaction 105 4.9 Extensions of the Jaynes–Cummings model 107 4.10 Schmidt decomposition and von Neumann entropy for the Jaynes–Cummings model 108 Problems 110 References 113 Bibliography 114 5 Quantum coherence functions 115 5.1 Classical coherence functions 115 5.2 Quantum coherence functions 120 5.3 Young’s interference 124 5.4 Higher-order coherence functions 127 Problems 133 References 133 Bibliography 134 6 Beam splitters and interferometers 135 6.1 Experiments with single photons 135 6.2 Quantum mechanics of beam splitters 137 6.3 Interferometry with a single photon 143 6.4 Interaction-free measurement 144 6.5 Interferometry with coherent states of light 146 Problems 147 References 149 Bibliography 149 7 Nonclassical light 150 7.1 Quadrature squeezing 150 7.2 Generation of quadrature squeezed light 165 7.3 Detection of quadrature squeezed light 167 7.4 Amplitude (or number) squeezed states 169 7.5 Photon antibunching 171 Contents ix 7.6 Schr¨odinger cat states 174 7.7 Two-mode squeezed vacuum states 182 7.8 Higher-order squeezing 188 7.9 Broadband squeezed light 189 Problems 190 References 192 Bibliography 194 8 Dissipative interactions and decoherence 195 8.1 Introduction 195 8.2 Single realizations or ensembles? 196 8.3 Individual realizations 200 8.4 Shelving and telegraph dynamics in three-level atoms 204 8.5 Decoherence 207 8.6 Generation of coherent states from decoherence: nonlinear optical balance 208 8.7 Conclusions 210 Problems 211 References 211 Bibliography 212 9 Optical test of quantum mechanics 213 9.1 Photon sources: spontaneous parametric down-conversion 214 9.2 The Hong–Ou–Mandel interferometer 217 9.3 The quantum eraser 219 9.4 Induced coherence 222 9.5 Superluminal tunneling of photons 224 9.6 Optical test of local realistic theories and Bell’s theorem 226 9.7 Franson’s experiment 232 9.8 Applications of down-converted light to metrology without absolute standards 233 Problems 235 References 236 Bibliography 237 10 Experiments in cavity QED and with trapped ions 238 10.1 Rydberg atoms 238 10.2 Rydberg atom interacting with a cavity field 241 10.3 Experimental realization of the Jaynes–Cummings model 246 10.4 Creating entangled atoms in CQED 249 10.5 Formation of Schr¨odinger cat states with dispersive atom–field interactions and decoherence from the quantum to the classical 250 10.6 Quantum nondemolition measurement of photon number 254 x Contents 10.7 Realization of the Jaynes–Cummings interaction in the motion of a trapped ion 255 10.8 Concluding remarks 258 Problems 259 References 260 Bibliography 261 11 Applications of entanglement: Heisenberg-limited interferometry and quantum information processing 263 11.1 The entanglement advantage 264 11.2 Entanglement and interferometric measurements 265 11.3 Quantum teleportation 268 11.4 Cryptography 270 11.5 Private key crypto-systems 271 11.6 Public key crypto-systems 273 11.7 The quantum random number generator 274 11.8 Quantum cryptography 275 11.9 Future prospects for quantum communication 281 11.10 Gates for quantum computation 281 11.11 An optical realization of some quantum gates 286 11.12 Decoherence and quantum error correction 289 Problems 290 References 291 Bibliography 293 Appendix A The density operator, entangled states, the Schmidt decomposition, and the von Neumann entropy 294 A.1 The density operator 294 A.2 Two-state system and the Bloch sphere 297 A.3 Entangled states 298 A.4 Schmidt decomposition 299 A.5 von Neumann entropy 301 A.6 Dynamics of the density operator 302 References 303 Bibliography 303 Appendix B Quantum measurement theory in a (very small) nutshell 304 Bibliography 307 Appendix C Derivation of the effective Hamiltonian for dispersive (far off-resonant) interactions 308 References 311 Contents xi Appendix D Nonlinear optics and spontaneous parametric down-conversion 312 References 313 Index 314 Acknowledgements This book developed out of courses that we have given over the years at Imperial College London, and the Graduate Center of the City University of New York, and we are grateful to the many students who have sat through our lectures and acted as guinea pigs for the material we have presented here. We would like to thank our many colleagues who, over many years have given us advice, ideas and encouragement. We particularly thank Dr. Simon Capelin at Cambridge University Press who has had much more confidence than us that this would ever be completed. Over the years we have benefited from many discussions with our colleagues, especially Les Allen, Gabriel Barton, Janos Bergou, Keith Burnett, Vladimir Buzek, Richard Campos, Bryan Dalton, Joseph Eberly, Rainer Grobe, Edwin Hach III, Robert Hilborn, Mark Hillery,Ed Hinds, Rodney Loudon, Peter Milonni, Bill Munro, Geoffrey New,Edwin Power, George Series, Wolfgang Schleich, Bruce Shore, Carlos Stroud Jr, Stuart Swain, Dan Walls and Krzysztof Wodkiewicz. We especially thank Adil Benmoussa for creating all the figures for this book using his expertise with Mathematica, Corel Draw, and Origin Graphics, for working through the homework problems, and for catching many errors in various drafts of the manuscript.
Load more

Recommended publications
  • Iupap 2011-2014 General Report
    TABLE OF CONTENTS I. ORGANISATION & AWARDS FOR EXCELLENCE 1 II. STATUTES & BYLAWS 9 Appendix A IUPAP International Commissions for the period 2011-2014 III. MINUTES OF THE 27th GENERAL ASSEMBLY 16 Appendix B List of Attendees Appendix C Presidential Address IV. RESOLUTIONS PASSED BY THE 2011 GENERAL ASSEMBLY 35 Appendix D Amendment to By-Law IIB Appendix E International Year of Light 2015 Appendix F Approval of Executive Council’s recommendations Appendix G Universality of Science resolution revised Appendix H International Association of Physics Students Appendix I Women in Physics Appendix J SESAME V. INTERNATIONAL CONFERENCES 44 VI. STATEMENT OF UNIVERSALITY OF SCIENCE 49 VII. IUPAP OFFICERS 50 Executive Council List of Former Presidents, Secretaries-General and Associate Secretaries- General List of Former Vice-Presidents VIII. LIAISON COMMITTEES, COMMISSIONS AND WORKING GROUPS 58 The Liaison Committees The International Commissions The International Affiliated Commissions The IUPAP Delegates to Inter-Union Commissions IUPAP Working Groups I – ORGANISATION & AWARDS FOR EXCELLENCE IUPAP was established in 1922 at Brussels with 13 Member countries. An outline of the history of IUPAP is given on the website (Document: IUPAP-70). The Union is composed of Members representing identified physics communities. Adhering bodies act through their Liaison Committees. Delegates from these Committees meet in the General Assemblies of the Union which are held every three years. The General Assembly appoints the Members of the Executive Council and
    [Show full text]
  • Principles of Optics
    Principles of optics Electromagnetic theory of propagation, interference and diffraction of light MAX BORN MA, Dr Phil, FRS Nobel Laureate Formerly Professor at the Universities of Göttingen and Edinburgh and EMIL WOLF PhD, DSc Wilson Professor of Optical Physics, University of Rochester, NY with contributions by A.B.BHATIA, P.C.CLEMMOW, D.GABOR, A.R.STOKES, A.M.TAYLOR, P.A.WAYMAN AND W.L.WILCOCK SEVENTH (EXPANDED) EDITION CAMBRIDGE UNIVERSITY PRESS Contents Historical introduction xxv I Basic properties of the electromagnetic field 1 1.1 The electromagnetic field 1 1.1.1 Maxwells equations 1 1.1.2 Material equations 2 1.1.3 Boundary conditions at a surface of discontinuity 4 1.1.4 The energy law of the electromagnetic field 7 1.2 The wave equation and the velocity of light 11 1.3 Scalar waves 14 1.3.1 Plane waves 15 1.3.2 Spherical waves 16 1.3.3 Harmonie waves. The phase velocity 16 1.3.4 Wave packets. The group velocity 19 1.4 Vector waves 24 1.4.1 The general electromagnetic plane wave 24 1.4.2 The harmonic electromagnetic plane wave 25 (a) Elliptic polarization 25 (b) Linear and circular polarization 29 (c) Characterization of the state of polarization by Stoltes parameters 31 1.4.3 Harmonie vector waves of arbitrary form 33 1.5 Reflection and refraction of a plane wave 38 1.5.1 The laws of reflection and refraction 38 1.5.2 Fresnel formulae 40 1.5.3 The reflectivity and transmissivity; polarization an reflection and refraction 43 1.5.4 Total reflection 49 1.6 Wave propagation in a stratified medium.
    [Show full text]
  • Colloquiumcolloquium
    ColloquiumColloquium History and solution of the phase problem in the theory of structure determination of crystals from X-ray diffraction experiments Emil Wolf Department of Physics and Astronomy Institute of Optics University of Rochester 3:45 pm, Wednesday, Nov 18, 2009 B.Sc. and Ph.D. Bristol University Baush & Lomb 109 D.Sc. University of Edinburgh U. of Rochester 1959 - Tea 3:30 B&L Lobby Wilson Professor of Optical Physics JointlyJointly sponsoredsponsored byby The most important researches carried out in this field will be reviewed and a recently DepartmentDepartment ofof PhysicsPhysics andand AstronomyAstronomy obtained solution of the phase problem will be presented. History and solution of the phase problem in the theory of structure determination of crystals from X-ray diffraction experiments Emil Wolf Department of Physics and Astronomy and The Institute of Optics University of Rochester Abstract Since the pioneering work of Max von Laue on interference and diffraction of X-rays carried out almost a hundred years ago, numerous attempts have been made to determine structures of crystalline media from X-ray diffraction experiments. Usefulness of all of them has been limited by the inability of measuring phases of the diffracted beams. In this talk the most important researches carried out in this field will be reviewed and a recently obtained solution of the phase problem will be presented. Biography Emil Wolf is Wilson Professor of Optical Physics at the University of Rochester, and is reknowned for his work in physical optics. He has received many awards, including the Ives Medal of the Optical Society of America, the Albert A.
    [Show full text]
  • A QED Framework for Nonlinear and Singular Optics
    A QED framework for nonlinear and singular optics A thesis submitted by: Matt M. Coles as part of the requirements for the degree of PhD in the School of Chemistry University of East Anglia Norwich NR4 7TJ © This copy of the thesis has been supplied on condition that anyone who consults it is understood to recognise that its copyright rests with the author and that no quotation from the thesis, nor any information derived therefrom, may be published without the author's prior, written consent. The research in this thesis has not been submitted previously for a degree at this or any other university. Except where explicitly mentioned, the work is of my own. M. M. Coles January 2014 Abstract The theory of quantum electrodynamics is employed in the description of linear and nonlinear optical effects. We study the effects of using a two energy level approximation in simplifying expressions obtained from perturbation theory, equivalent to truncating the completeness relation. However, applying a two-level model with a lack of regard for its domain of validity may deliver misleading results. A new theorem on the expectation values of analytical operator functions imposes additional constraints on any atom or molecule modelled as a two-level system. We introduce measures designed to indicate occasions when the two-level approximation may be valid. Analysis of the optical angular momentum operator delivers a division into spin and orbital parts satisfying electric-magnetic democracy, and determine a new compartmentalisation of the optical angular momentum. An analysis is performed on the recently rediscovered optical chirality, and its corresponding flux, delivering results proportional to the helicity and spin angular momentum in monochromatic beams.
    [Show full text]
  • Number-Coherent States 55
    Open Research Online The Open University’s repository of research publications and other research outputs Quantum optical states and Bose-Einstein condensation : a dynamical group approach Thesis How to cite: Feng, Yinqi (2001). Quantum optical states and Bose-Einstein condensation : a dynamical group approach. PhD thesis The Open University. For guidance on citations see FAQs. c 2001 The Author https://creativecommons.org/licenses/by-nc-nd/4.0/ Version: Version of Record Link(s) to article on publisher’s website: http://dx.doi.org/doi:10.21954/ou.ro.0000d4a8 Copyright and Moral Rights for the articles on this site are retained by the individual authors and/or other copyright owners. For more information on Open Research Online’s data policy on reuse of materials please consult the policies page. oro.open.ac.uk Quantum Optical States and Bose-Einstein Condensation: A Dynamical Group Approach Yinqi Feng A thesis submitted for the degree of Doctor of Philosophy in the Faculty of Mathematics and Computing of The Open University May,2001 Contents Abstract vii Acknowledgements ix Introduction 1 I Quantum Optical States and Dynamical Groups 5 1 Displaced and Squeezed Number States 6 1.1 Conventional Coherent and Squeezed States ...... 6 1.1.1 Coherent States . ...... 8 1.1.2 Squeezed States . ........ 9 1.1.3 Group-theoretical Description . ..... 12 1.2 Photon Number States ....... ..... 19 1.2.1 Displaced Number States .. ..... 19 1.2.2 Squeezed Number States . 22 1.2.3 Displaced Squeezed Phase Number States (DSPN states) 24 1.3 Optimal Signal-to-Quantum Noise Ratio ............. 26 i 2 Kerr States and Squeezed Kerr States(q-boson Analogue) 32 2.1 Kerr States .
    [Show full text]
  • Download Principles of Physical Optics 1St Edition Free Ebook
    PRINCIPLES OF PHYSICAL OPTICS 1ST EDITION DOWNLOAD FREE BOOK Charles A Bennett | --- | --- | --- | 9780470122129 | --- | --- Principles Of Adaptive Optics If you wish to place a tax exempt order please contact us. He has collaborated with Oak Ridge National Laboratory sincewhere he is currently an adjunct research and development associate Principles of Physical Optics 1st edition the Advanced Laser and Optical Technology and Development group. Magnetic Lenses. Connect with:. A beginning might be the recalling of one's career-long association with it. All Pages Books Journals. When I asked for it, he argued that as a theorist he had a greater need for the book than I, an experimentalist, did. Principles of Physical Optics Bennett, Charles a. Complete Electron Guns. Search icon An illustration of a magnifying glass. Physical Optics. This includes detailed discussions on geometric optics, superposition and interference, and diffraction. Institutional Subscription. If you wish to place a tax exempt order please Principles of Physical Optics 1st edition us. This includes detailed discussions on. Breathing a breath of fresh air into the field of optics, Principles of Principles of Physical Optics 1st edition Optics is the first new entry in the field in the last 20 years. Another colleague borrowed my newly-purchased copy and was slow to return it. Readers will also find the latest information on lasers, optical imaging, polarization, and nonlinear optics. Seller Rating:. Thanks in advance for your time. Systematically describes a number of sub-topics in the field. About the Author Charles A. In physical optics, the wave property of light is considered. Additional Collections.
    [Show full text]
  • Arxiv:1812.03158V1 [Quant-Ph] 7 Dec 2018
    Generation and sampling of quantum states of light in a silicon chip Stefano Paesani,1, ∗ Yunhong Ding,2, 3, y Raffaele Santagati,1 Levon Chakhmakhchyan,1 Caterina Vigliar,1 Karsten Rottwitt,2, 3 Leif K. Oxenløwe,2, 3 Jianwei Wang,1, 4, z Mark G. Thompson,1, x and Anthony Laing1, { 1Quantum Engineering Technology Labs, H. H. Wills Physics Laboratory and Department of Electrical and Electronic Engineering, University of Bristol, BS8 1FD, Bristol, United Kingdom 2Department of Photonics Engineering, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark 3Center for Silicon Photonics for Optical Communication (SPOC), Technical University of Denmark, 2800 Kgs. Lyngby, Denmark 4State Key Laboratory for Mesoscopic Physics and Collaborative Innovation Center of Quantum Matter, School of Physics, Peking University, Beijing 100871, China (Dated: December 10, 2018) Implementing large instances of quantum algorithms requires the processing of many quantum information carriers in a hardware platform that supports the integration of different components. While established semiconductor fabrication processes can integrate many photonic components, the generation and algorithmic processing of many photons has been a bottleneck in integrated photonics. Here we report the on-chip generation and processing of quantum states of light with up to eight photons in quantum sampling algorithms. Switching between different optical pumping regimes, we implement the Scattershot, Gaussian and standard boson sampling protocols in the same silicon chip, which integrates linear and nonlinear photonic circuitry. We use these results to benchmark a quantum algorithm for calculating molecular vibronic spectra. Our techniques can be readily scaled for the on-chip implementation of specialised quantum algorithms with tens of photons, pointing the way to efficiency advantages over conventional computers.
    [Show full text]
  • Introductory Quantum Optics Christopher Gerry and Peter Knight Frontmatter More Information
    Cambridge University Press 052152735X - Introductory Quantum Optics Christopher Gerry and Peter Knight Frontmatter More information Introductory Quantum Optics This book provides an elementary introduction to the subject of quantum optics, the study of the quantum-mechanical nature of light and its interaction with matter. The presentation is almost entirely concerned with the quantized electromag- netic field. Topics covered include single-mode field quantization in a cavity, quantization of multimode fields, quantum phase, coherent states, quasi- probability distribution in phase space, atom–field interactions, the Jaynes– Cummings model, quantum coherence theory, beam splitters and interferom- eters, nonclassical field states with squeezing etc., tests of local realism with entangled photons from down-conversion, experimental realizations of cavity quantum electrodynamics, trapped ions, decoherence, and some applications to quantum information processing, particularly quantum cryptography. The book contains many homework problems and a comprehensive bibliography. This text is designed for upper-level undergraduates taking courses in quantum optics who have already taken a course in quantum mechanics, and for first- and second-year graduate students. A solutions manual is available to instructors via [email protected]. Christopher Gerry is Professor of Physics at Lehman College, City Uni- versity of New York.He was one of the first to exploit the use of group theoretical methods in quantum optics and is also a frequent contributor to Physical Review A. In 1992 he co-authored, with A. Inomata and H. Kuratsuji, Path Integrals and Coherent States for Su (2) and SU (1, 1). Peter Knight is a leading figure in quantum optics, and in addition to being President of the Optical Society of America in 2004, he is a Fellow of the Royal Society.
    [Show full text]
  • Conceptualization of the Casimir Effect
    INSTITUTE OF PHYSICS PUBLISHING EUROPEAN JOURNAL OF PHYSICS Eur. J. Phys. 22 (2001) 447–451 www.iop.org/Journals/ej PII: S0143-0807(01)23822-7 Conceptualization of the Casimir effect D L Andrews andLCDavila´ Romero School of Chemical Sciences, University of East Anglia, Norwich NR4 7TJ, UK E-mail: [email protected] Received 10 April 2001 Abstract The origins and physical significance of the Casimir effect are reviewed, linking the zero-point energy of the vacuum in quantum electrodynamics with a force between conducting plates. It is shown how, by the use of dimensional and other simple physical arguments, the major features of the phenomenon can be derived. 1. Introduction Hendrik Brugt Gerhard Casimir, whose name is known throughout the physics world, died on 4 May 2000. This brief article written in his honour concerns the discovery, formulation, physical significance and impact of one of the phenomena that bears his name, the eponymous Casimir effect. The discovery of this fundamental and very general effect is remarkable in the history of science for a host of reasons, and there is an extensive literature on the subject. To quote his original publication, ‘there exists an attractive force between two metal plates which is independent of the material of the plates...’, qualified by the condition that the intervening distance is sufficiently large ‘...that for the wavelengths comparable with that distance the penetration depth is small compared with the distance’. Such an attraction between two metal plates in vacuum has nothing to do with the forces of gravity or electrostatics. ‘This force may be interpreted as a zero point pressure of electromagnetic waves’ [1].
    [Show full text]
  • Snowpack Optical Properties in the Infrared
    BUREAU OF RECLAMATION LIBRARY REPORT 79-11 Snowpack optical properties in the infrared 70 s ~ <S> \ * *=> l,***»r AUb?8 1979 'ZSSSff* For conversion of SI metric units to U.S./British customary units of measurement consult ASTM Standard E380, Metric Practice Guide, published by the American Society for Testing and Materials, 1916 Race St., Philadelphia, Pa. 19103. BUREAU OF RECLAMATION DENVER U6RARY 92028164 isoEfiim ■ ^ ^ l RREL Report 79-11 Oi Snowpack optical properties in the infrared Roger H. Berger May 1979 Prepared for DIRECTORATE OF MILITARY PROGRAMS OFFICE, CHIEF OF ENGINEERS By UNITED STATES ARMY CORPS OF ENGINEERS COLD REGIONS RESEARCH AND ENGINEERING LABORATORY HANOVER, NEW HAMPSHIRE, U.S.A. Approved for public release; distribution unlimited. Unclassified SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) READ INSTRUCTIONS REPORT DOCUMENTATION PAGE BEFORE COMPLETING FORM 1. R E P O R T N U M B E R 2. GOVT ACCESSION NO. 3. RECIPIENTS CATALOG-NUMBER ' -G R R E L 1 Report 79-11 4. T IT L E (and Subtitle) J 5. TYPE OF REPORT & PERIOD COVERED 3 SNOWPACK OPTICAL PROPERTIES IN THE INFRARED 6. PERFORMING ORG. REPORT NUMBER 7. AUTHOR!» 8. CONTRACT OR GRANT NUMBER!» Roger H. Berger s 9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT, PROJECT, TASK A R E A & WORK UNIT NUMBERS U .S.% rny Cold Regions Research and Engineering Labefatury™ DA Project 4A762730AT42 Hanover, New Hampshire 03755 ^ Technical Area A1, Work Unit 004 11. CONTROLLING OFFICE NAME AND ADDRESS 12. R E P O R T D A T E Directorate of Military Programs ^ May 1979 Office, Chief of Engineers 13.
    [Show full text]
  • Arxiv:1604.01800V1 [Physics.Optics]
    BIREFRINGENCE PHENOMENA REVISITED Dante D. Pereira1, Baltazar J. Ribeiro2 and Bruno Gon¸calves3 1Centro Federal de Educa¸c˜ao Tecnol´ogica Celso Suckow da Fonseca CEFET-RJ, 27.600-000, Valen¸ca, Rio de Janeiro, Brazil 2Centro Federal de Educa¸c˜ao Tecnol´ogica de Minas Gerais CEFET-MG, 37.250-000, Nepomuceno, Minas Gerais, Brazil 3Instituto Federal de Educa¸c˜ao, Ciˆencia e Tecnologia do Sudeste de Minas Gerais IF Sudeste MG, 36080-001, Juiz de Fora, Minas Gerais, Brazil Abstract The propagation of electromagnetic waves is investigated in the context of the isotropic and nonlinear dielectric media at rest in the eikonal limit of the geometrical optics. Taking into account the functional dependence ε = ε(E,B) and µ = µ(E,B) for the dielectric coefficients, a set of phenomena related to the birefringence of the electromagnetic waves induced by external fields are derived and discussed. Our results contemplate the known cases already reported in the literature: Kerr, Cotton-Mouton, Jones and magnetoelectric effects. Moreover, new effects are presented here as well as the perspectives of its experimental confirmations. PACS numbers: 03.50.De, 04.20.-q, 42.25.Lc 1 Introduction Electromagnetic waves in nonlinear media propagate according to Maxwell’s equations com- plemented by certain phenomenological constitutive relations linking strengths and induced fields [1]. Depending on the dielectric properties of the medium and also on the presence of applied external fields, a variety of optical effects can be found. One of such an effects which has received significant attention of the scientific community in the last years is the birefringence phenomenon (or duble refraction) [2, 3].
    [Show full text]
  • Fundamentals
    1 Fundamentals 1.1. CHARACTERISTICS OF FEMTOSECOND LIGHT PULSES Femtosecond (fs) light pulses are electromagnetic wave packets and as such are fully described by the time and space dependent electric field. In the frame of a semiclassical treatment the propagation of such fields and the interaction with matter are governed by Maxwell’s equations with the material response given by a macroscopic polarization. In this first chapter we will summarize the essential notations and definitions used throughout the book. The pulse is characterized by measurable quantities that can be directly related to the electric field. A complex representation of the field amplitude is particularly convenient in dealing with propagation problems of electromagnetic pulses. The next section expands on the choice of field representation. 1.1.1. Complex Representation of the Electric Field Let us consider first the temporal dependence of the electric field neglecting its spatial and polarization dependence, i.e., E(x, y, z, t) = E(t). A complete description can be given either in the time or the frequency domain. Even though the measured quantities are real, it is generally more convenient to use complex representation. For this reason, starting with the real E(t), one defines the complex 1 2 Fundamentals spectrum of the field strength E˜ (), through the complex Fourier transform (F): ∞ − E˜ () = F {E(t)} = E(t)e itdt =|E˜ ()|ei() (1.1) −∞ In the definition (1.1), |E˜ ()| denotes the spectral amplitude, and ()isthe spectral phase. Here and in what follows, complex quantities related to the field are typically written with a tilde. Because E(t) is a real function, E˜ () = E˜ ∗(−) holds.
    [Show full text]